以馬可夫決策過程分析隨機需求下訂單生產系統動態訂料之研究

Optimal Ordering Policy for a MTO System with Random Demand and Lead Time – a Markov Decision Process Approach

王毅斌(Yi-Bing Wang)

指導教授 ： 張國華

中原大學/工學院/工業工程研究所/碩士(2004年)

https://doi.org/10.6840/cycu200400289

摘要

現行的生產管理系統，主要可分為計畫式(Make-to-stock, MTS)生產、訂單
式(Make-to-order, MTO)生產。近年來產業環境型態逐漸改變，許多產業將部份
的生產方式由計畫式改為訂單式。在訂單式生產系統中，由於需求的不確定性，
對於原物料的庫存掌控不易: 過少的庫存易造成訂單的流失或延遲交貨的情
形，過多的庫存會造成資金的積壓或是呆料的情形。
面對不定性的需求，為了避免造成以上的成本損失，傳統的控制庫存方式如
需求預測與靜態控制應逐漸轉變為動態地控制庫存量。面對龐大複雜的系統，若
只依據個人經驗與直覺無法完善的管理，需要藉由數量化的方式輔助管理決策。
本篇論文考慮一個訂單式生產系統，此生產系統具有隨機需求與隨機前置時
間。在這兩個不確定性的因素下，我們將以動態控制的方式最佳化此系統。本研
究將此生產系統視為一個等候系統，藉由觀察系統內等候的需求數量與系統的原
物料庫存量來決定是否訂購原物料，以最小化系統的總成本。對本論文所探討的
系統，我們以馬可夫決策過程(Markov decision process, MDP)分析之。研究中發
現，當系統成本函數滿足某些條件時，系統的最佳訂購策略具有threshold 的
結構。

關鍵字

庫存控制 ； 馬可夫決策過程 ； 訂購策略 ； 等候系統

並列摘要

Production system can be distinguished as Make-to-Stock (MTS) or Make-to-
Order (MTO) system. In MTO system, we usually confront the random demands.
Because of the uncertainty of demands, it is important to control the inventory of raw
materials such as determining the ordering epoch and order quantity. Also because of
the uncertainty of the demands, it is natural have the dynamic ordering epoch. The
traditional approaches such as forecasting and static inventory control are replaced by
dynamic control. This thesis studies the dynamic material ordering policy for MTO
production system with random demand.
We consider a simple MTO system with demand queue and raw material inventory
and constant ordering quantity with random ordering lead time. We treat
this system as a queueing system and we model the underlying problem as a Markov
decision process(MDP), in which, we determine the ordering epoch by observing the
current state of system. We seek to find the optimal policy to to minimize system
cost. Under some normal conditions, the optimal policy is proven to be a threshold
policy; furthermore, the optimal policy can be characterized by the switching curve.
Some numerical examples are provided.

並列關鍵字

Make-to-order production system ； Markov decision ； Queueing system

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